The problem states that the sum of the roots of the equation $(x - p)(2x + 1) = 0$ is 1. We need to find the value of $p$.

1. Problem Description

The problem states that the sum of the roots of the equation $(x - p)(2x + 1) = 0$ is

1. We need to find the value of $p$.

2. Solution Steps

First, we need to find the roots of the equation $(x - p)(2x + 1) = 0$. The roots are the values of $x$ that make the equation true.

The roots are found by setting each factor to zero:

$x - p = 0$, which gives $x = p$.

$2x + 1 = 0$, which gives $2x = -1$, so $x = -\frac{1}{2}$.

Thus, the roots are $p$ and $-\frac{1}{2}$.

The problem states that the sum of the roots is

1. Therefore,

$p + (-\frac{1}{2}) = 1$.

$p - \frac{1}{2} = 1$.

Adding $\frac{1}{2}$ to both sides, we get

$p = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}$.

$p = \frac{3}{2} = 1\frac{1}{2}$.

3. Final Answer

The value of $p$ is $1\frac{1}{2}$.

Therefore, the answer is A. $1\frac{1}{2}$.